If |n + 5| = 5, what is the value of n?

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Given |n+5| = 5 , this means that either n=0 or n =-10 and the question asks us what is the value of n?

Per statement 1, \(n^2\) \(\neq\)0 ---> n\(\neq\) 0 ---> n = -10 is the only value possible. Thus this statement is sufficient.

Per statement 2, \(n^2\)+10n=0 --> n(n+10) = 0 ---> either n = 0 or n = -10. This still does not give 1 unique value. This statement is not sufficient.

A is the correct answer.

Given: | n + 5 | = 5 => (n+5) = 5 or -5. Hence n = 0 or -10
Required: n =? This means we have to find a definitive value of n

Statement 1: \(n^{2}\) ≠ 0
Hence n ≠ 0.
This leaves us with only one value of n = -10.

SUFFICIENT

Statement 2:
\(n^{2}\) + 10n = 0
or n(n + 10) = 0
This gives us n = 0 and -10.
Still we do not have a unique value of n

INSUFFICIENT

So, the correct answer is A

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

If |n + 5| = 5, what is the value of n?

(1) n^2 is not equal to 0.
(2) n^2 + 10n = 0.


Transforming the original codntiion we have n+5=-5,5, n=-10,0. Since there is 1 variable (n), we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), since n is not 0, n = 10 this is a unique answer and therefore is sufficient.
In case of 2), n(n+10)=0, n=0,-10 therefore it is not unique. Thus it is not sufficient.
The answer is A.

Solution:
Given: |n + 5| = 5
Inferences: |n + 5| = 5, this means we can get two cases here;
A. n + 5 = 5
n = 0

B. n + 5 = -5
n = -10
Therefore |n + 5| = 5 will be true when n = 0 or -10.
To find: The value of “n”.

Analysis of statement 1: \(n^2\) is not equal to 0.
\(n^2\) ≠0; this means that, n ≠0.
Therefore n value must be “-10”.
Hence statement 1 is sufficient to answer. We can eliminate options B, C and E.

Analysis of statement 2: \(n^2+ 10n=0\)
\(n^2+ 10n=0\)
\(n (n+10)= 0\)
This means n = 0 or n = -10
We are getting two values for “n”, hence statement 2 is insufficient. So we can eliminate option D.

The correct answer option is “A”.

Two ways to approach absolute value

n +5 =5
n =0

-ln +5l =5
-n -5 =5
-n =10
n= -10

Stmnt 1

Suff because it cannot be the other x value

Stmnt 2

n( n +10) =0

n =- 10, n =0

Insuff

A

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